Highest Common Factor of 866, 2552, 9991 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 866, 2552, 9991 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 866, 2552, 9991 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 866, 2552, 9991 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 866, 2552, 9991 is 1.
HCF(866, 2552, 9991) = 1
HCF of 866, 2552, 9991 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 866, 2552, 9991 is 1.
Highest Common Factor of 866,2552,9991 is 1
Step 1: Since 2552 > 866, we apply the division lemma to 2552 and 866, to get
2552 = 866 x 2 + 820
Step 2: Since the reminder 866 ≠ 0, we apply division lemma to 820 and 866, to get
866 = 820 x 1 + 46
Step 3: We consider the new divisor 820 and the new remainder 46, and apply the division lemma to get
820 = 46 x 17 + 38
We consider the new divisor 46 and the new remainder 38,and apply the division lemma to get
46 = 38 x 1 + 8
We consider the new divisor 38 and the new remainder 8,and apply the division lemma to get
38 = 8 x 4 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 866 and 2552 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(38,8) = HCF(46,38) = HCF(820,46) = HCF(866,820) = HCF(2552,866) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9991 > 2, we apply the division lemma to 9991 and 2, to get
9991 = 2 x 4995 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 9991 is 1
Notice that 1 = HCF(2,1) = HCF(9991,2) .
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Frequently Asked Questions on HCF of 866, 2552, 9991 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 866, 2552, 9991?
Answer: HCF of 866, 2552, 9991 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 866, 2552, 9991 using Euclid's Algorithm?
Answer: For arbitrary numbers 866, 2552, 9991 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.